Abstract

Probabilistic models such as logistic regression, Bayesian classification, neural networks, and models for natural language processing, are increasingly more present in both undergraduate and graduate statistics and data science curricula due to their wide range of applications. In this paper, we present a one-week course module for studnets in advanced undergraduate and applied graduate courses on variational inference, a popular optimization-based approach for approximate inference with probabilistic models. Our proposed module is guided by active learning principles: In addition to lecture materials on variational inference, we provide an accompanying class activity, an R shiny app, and guided labs based on real data applications of logistic regression and clustering documents using Latent Dirichlet Allocation with R code. The main goal of our module is to expose students to a method that facilitates statistical modeling and inference with large datasets. Using our proposed module as a foundation, instructors can adopt and adapt it to introduce more realistic case studies and applications in data science, Bayesian statistics, multivariate analysis, and statistical machine learning courses.

摘要

由于其广泛的应用，逻辑回归、贝叶斯分类、神经网络和自然语言处理模型等概率模型越来越多地出现在本科生和研究生的统计学和数据科学课程中。在本文中，我们为高级本科生和应用研究生课程的学生提供了为期一周的变分推理课程模块，变分推理是一种流行的基于优化的概率模型近似推理方法。我们提出的模块以主动学习原则为指导：除了有关变分推理的讲座材料之外，我们还提供了随附的课堂活动、R 闪亮应用程序以及基于逻辑回归和聚类文档的实际数据应用的指导实验，其中使用潜在狄利克雷分配R 代码。我们模块的主要目标是让学生了解一种有助于对大型数据集进行统计建模和推理的方法。以我们提出的模块为基础，教师可以采用和调整它来介绍数据科学、贝叶斯统计、多元分析和统计机器学习课程中更现实的案例研究和应用。